If each observation in a data set for number of employees in different divisions is doubled then the coefficient of quartile deviation:

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  1. is also doubled
  2. is fourtimes of the original
  3. is halved
  4. remains same

Answer (Detailed Solution Below)

Option 4 : remains same
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The correct answer is that it remains same.

Key Points 

 The formulae we need for solving the problem are as follows:

Quartile formula for Q1,grouped data=Q1=I1+(N/4)cf(I2I1)Quartile formula for Q3,grouped data=Q3=I1+3(N/4)cf(I2I1)Coefficient of quartile deviation=Q3Q1Q3+Q1

Here, since all the observations are doubled the value for Quartiles becomes:

Quartile formula for Q1,grouped data=Q1=I1+(2N/4)2c2f(I2I1)Quartile formula for Q1,grouped data=Q1=I1+(N/4)cf(I2I1)Quartile formula for Q3,grouped data=Q3=I1+3(2N/4)2c2f(I2I1)Quartile formula for Q3,grouped data=Q3=I1+3(N/4)cf(I2I1)Coefficient of quartile deviation=Q3Q1Q3+Q1

This is the same value as the coefficient of quartile deviation when the values of the observation of the data set were unchanged.

Thus the correct answer is- If each observation in a data set for the number of employees in different divisions is doubled then the coefficient of quartile deviation remains same.

Additional Information

  •  The formula in this case used is for grouped data as the question specifically says observation of different employees for different departments.
  • The same result can be derived for ungrouped data as well.
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